Through a vertically shrinking sheet, a two-dimensional magnetic nanofluid is numerically analyzed for convection, heat generation and absorption, and the slip velocity effect. In this research, Al2O3-Cu/water composite nanofluid is studied, where water is deemed the base liquid and copper (Cu) and alumina (Al2O3) are the solid nanoparticles. Modern composite nanofluids improve heat transfer efficiency. Using the Tiwari-Das model, the current study examines the effects of the solid volume fraction of copper, heat generation/absorption, MHD, mixed convection, and velocity slip parameters on velocity and temperature distributions. Introducing exponential similarity variables converts nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). MATLAB bvp4c solver is used to solve ODEs. Results showed dual solutions for suction with 0%-10% copper nanoparticles and 1%-500% heat generation/absorption. As copper (Cu) solid volume percentage increases from 0% to 10%, reduced skin friction f ″ ( 0 ) boosts in the first solution but falls in the second. When Cu is added to both solutions, heat transport - θ ' ( 0 ) decreases. As heat generation/absorption increases 1%-500%, - θ ' ( 0 ) decreases in both solutions. In conclusion, solution dichotomy exists when suction parameter S ≥ S c i in assisting flow case, while no fluid flow is possible when S < S c i .